*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 17 Dec 2010 11:56:07 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/17/t12925868372nyj7vj77n2vnl3.htm/, Retrieved Fri, 17 Dec 2010 12:54:00 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/17/t12925868372nyj7vj77n2vnl3.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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101.82 107.34 93.63 99.85 101.76 101.68 107.34 93.63 99.91 102.37 101.68 107.34 93.63 99.87 102.38 102.45 107.34 96.13 99.86 102.86 102.45 107.34 96.13 100.10 102.87 102.45 107.34 96.13 100.10 102.92 102.45 107.34 96.13 100.12 102.95 102.45 107.34 96.13 99.95 103.02 102.45 112.60 96.13 99.94 104.08 102.52 112.60 96.13 100.18 104.16 102.52 112.60 96.13 100.31 104.24 102.85 112.60 96.13 100.65 104.33 102.85 112.61 96.13 100.65 104.73 102.85 112.61 96.13 100.69 104.86 103.25 112.61 96.13 101.26 105.03 103.25 112.61 98.73 101.26 105.62 103.25 112.61 98.73 101.38 105.63 103.25 112.61 98.73 101.38 105.63 104.45 112.61 98.73 101.38 105.94 104.45 112.61 98.73 101.44 106.61 104.45 118.65 98.73 101.40 107.69 104.80 118.65 98.73 101.40 107.78 104.80 118.65 98.73 100.58 107.93 105.29 118.65 98.73 100.58 108.48 105.29 114.29 98.73 100.58 108.14 105.29 114.29 98.73 100.59 108.48 105.29 114.29 98.73 100.81 108.48 106.04 114.29 101.67 100.75 108.89 105.94 114.29 101.67 100.75 108.93 105.94 114.29 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation vrijetijdsbesteding[t] = + 65.5701318446327 + 0.0934667042792763bios[t] + 0.112234682723702schouwburg[t] + 0.249400535389239eedagsacttractie[t] -0.0908956030942088huurDVD[t] + 0.0138828910919104M1[t] + 0.21346897571974M2[t] + 0.0879754877109333M3[t] -0.430673994391876M4[t] -0.555903351928635M5[t] -0.405997260390775M6[t] -0.421124427936515M7[t] -0.287961409775444M8[t] + 0.155647169325642M9[t] + 0.140501903035055M10[t] + 0.00744480645675077M11[t] + 0.173955632165732t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 65.5701318446327 7.813237 8.3922 0 0 bios 0.0934667042792763 0.020909 4.4701 6.1e-05 3e-05 schouwburg 0.112234682723702 0.035874 3.1285 0.00323 0.001615 eedagsacttractie 0.249400535389239 0.053145 4.6928 3e-05 1.5e-05 huurDVD -0.0908956030942088 0.090236 -1.0073 0.319695 0.159848 M1 0.0138828910919104 0.203923 0.0681 0.946054 0.473027 M2 0.21346897571974 0.206838 1.0321 0.308095 0.154047 M3 0.0879754877109333 0.210591 0.4178 0.678305 0.339153 M4 -0.430673994391876 0.270129 -1.5943 0.118544 0.059272 M5 -0.555903351928635 0.269783 -2.0606 0.045728 0.022864 M6 -0.405997260390775 0.269908 -1.5042 0.140194 0.070097 M7 -0.421124427936515 0.271415 -1.5516 0.128447 0.064223 M8 -0.287961409775444 0.272373 -1.0572 0.296595 0.148298 M9 0.155647169325642 0.205308 0.7581 0.452718 0.226359 M10 0.140501903035055 0.199681 0.7036 0.485639 0.242819 M11 0.00744480645675077 0.208953 0.0356 0.971751 0.485876 t 0.173955632165732 0.015756 11.0406 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.99899740753351 R-squared 0.997995820258674 Adjusted R-squared 0.99721370133523 F-TEST (value) 1276.01543747808 F-TEST (DF numerator) 16 F-TEST (DF denominator) 41 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.294272762981154 Sum Squared Residuals 3.55045482033506 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.76 101.597467200706 0.162532799293738 2 102.37 101.952469842715 0.417530157285066 3 102.38 102.004567810996 0.375432189004368 4 102.86 102.356253617858 0.503746382142368 5 102.87 102.383164947744 0.486835052256009 6 102.92 102.707026671448 0.212973328552414 7 102.95 102.864037224006 0.0859627759943083 8 103.02 103.186608126859 -0.166608126858517 9 104.08 104.395435725283 -0.315435725282948 10 104.16 104.538973815715 -0.378973815715032 11 104.24 104.5680559229 -0.328055922900215 12 104.33 104.734506255969 -0.404506255969322 13 104.73 104.923467126054 -0.193467126054197 14 104.86 105.293373018724 -0.433373018723994 15 105.03 105.327411350829 -0.29741135082893 16 105.62 105.631158892904 -0.0111588929038721 17 105.63 105.668977695162 -0.0389776951615503 18 105.63 105.992839418865 -0.362839418865142 19 105.94 106.26382792862 -0.323827928620263 20 106.61 106.565492842761 0.0445071572385886 21 107.69 107.864590361803 -0.174590361803161 22 107.78 108.056114074176 -0.276114074176048 23 107.93 108.171547004301 -0.241547004300722 24 108.48 108.383856515107 0.0961434848934477 25 108.14 108.082351821689 0.0576481783111435 26 108.48 108.454984582451 0.0250154175485287 27 108.48 108.483449693928 -0.00344969392767098 28 108.89 108.94754718243 -0.057547182430068 29 108.93 108.986926786631 -0.0569267866311065 30 109.21 109.291700433685 -0.0817004336849282 31 109.47 109.418715437222 0.0512845627780594 32 109.8 109.727617217983 0.0723827820173901 33 111.73 111.394837510485 0.335162489515496 34 111.85 111.595467423562 0.254532576437494 35 112.12 111.725159328215 0.394840671784764 36 112.15 111.907328094545 0.242671905454962 37 112.17 112.0833501894 0.086649810599563 38 112.67 112.496070788956 0.173929211044258 39 112.8 112.530898592649 0.26910140735146 40 113.44 113.749946099602 -0.309946099601988 41 113.53 113.795036550107 -0.265036550107189 42 114.53 114.160958290736 0.369041709263545 43 114.51 114.28433747015 0.225662529850298 44 115.05 114.944991661759 0.105008338241167 45 116.67 116.367933818383 0.30206618161678 46 117.07 116.702521296935 0.367478703065479 47 116.92 116.745237744584 0.174762255416174 48 117 116.934309134379 0.0656908656209122 49 117.02 117.13336366215 -0.113363662150248 50 117.35 117.533101767154 -0.183101767153859 51 117.36 117.703672551599 -0.343672551599227 52 117.82 117.945094207206 -0.125094207206439 53 117.88 118.005894020356 -0.125894020356163 54 118.24 118.377475185266 -0.137475185265889 55 118.5 118.539081940002 -0.0390819400024026 56 118.8 118.855290150639 -0.0552901506386285 57 119.76 119.907202584046 -0.147202584046167 58 120.09 120.056923389612 0.033076610388107 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.778370160732379 0.443259678535243 0.221629839267621 21 0.65524922208413 0.689501555831741 0.34475077791587 22 0.659685025455613 0.680629949088775 0.340314974544387 23 0.723536694677497 0.552926610645006 0.276463305322503 24 0.730703536989123 0.538592926021754 0.269296463010877 25 0.68517664234341 0.62964671531318 0.31482335765659 26 0.596420443290629 0.807159113418742 0.403579556709371 27 0.492539212568866 0.985078425137732 0.507460787431134 28 0.784362095430275 0.431275809139449 0.215637904569725 29 0.810358517774808 0.379282964450384 0.189641482225192 30 0.7552229583016 0.489554083396801 0.2447770416984 31 0.845962144469959 0.308075711060083 0.154037855530041 32 0.79022784446969 0.419544311060618 0.209772155530309 33 0.785701148536538 0.428597702926923 0.214298851463462 34 0.852491217869416 0.295017564261168 0.147508782130584 35 0.761412253942013 0.477175492115974 0.238587746057987 36 0.653177116653854 0.693645766692291 0.346822883346146 37 0.570194336759361 0.859611326481278 0.429805663240639 38 0.442244381770368 0.884488763540736 0.557755618229632 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

Parameters (R input):

par1 = 5 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = no ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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